Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Classification of circle actions on $ 4$-manifolds

Author: Ronald Fintushel
Journal: Trans. Amer. Math. Soc. 242 (1978), 377-390
MSC: Primary 57S15
MathSciNet review: 496815
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This article studies locally smooth $ {S^1}$-actions on closed oriented 4-manifolds in terms of the orbit space, orbit type data, and the characteristic class of the action which lies in $ {H_1}({M^{\ast}},{S^{\ast}})$ where $ {M^{\ast}}$ is the orbit space and $ {S^{\ast}}$ is the image of a certain collection of singular orbits. It is proved that such actions are determined by their weighted orbit spaces and are in 1-1 correspondence with ``legally-weighted'' 3-manifolds. The information contained in the weighted orbit space is used to give a presentation of the fundamental group of the 4-manifold, and in certain cases the quadratic form is computed.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57S15

Retrieve articles in all journals with MSC: 57S15

Additional Information

Keywords: 4-manifold, group action, orbit space, quadratic form
Article copyright: © Copyright 1978 American Mathematical Society